In order to construct possible candidates for \(O(x)\)  we need to know the operator content of the theory. A subset of these operators can be taken to be the momentum-space creation-annihilation operators which create asymptotic physical states with finite energy. Now, an important lesson following from our current understanding of soft-theorem – Ward identity correspondence is that we should also add to this list the soft operators \(S_{\alpha }(x)\)  [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}. They are usually defined as,
\(S_{\alpha }(x) = \displaystyle \lim _{\omega \rightarrow 0} D(\omega ) A(\omega ,x,\alpha )\) 
